Given n=20 observations: [1] 17.62080276 2.03655884 16.97386526 4.25347789 1.83408051 5.86805486 [7] 2.15020940 7.85805617 0.44024483 4.40750353 5.58303948...

Given n=20 observations:

[1] 17.62080276 2.03655884 16.97386526 4.25347789 1.83408051 5.86805486
[7] 2.15020940 7.85805617 0.44024483 4.40750353 5.58303948 10.95875446
[13] 2.74305620 6.87251402 0.03215674 4.79053522 14.19978116 10.01379904
[19] 10.94377572 2.44097982

It is suggested that these observations follow an exponential distribution. Test the hypothesis that these are observations of an exponential distribution using the chi-square test. Draw conclusions. Thanks.

Solutions

Expert Solution

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: C1

Observed and Expected Counts

Category	Observed	Test Proportion	Expected	Contribution to Chi-Square
1	17.6208	0.05	6.60106	18.3962
2	2.0366	0.05	6.60106	3.1563
3	16.9739	0.05	6.60106	16.2997
4	4.2535	0.05	6.60106	0.8349
5	1.8341	0.05	6.60106	3.4425
6	5.8681	0.05	6.60106	0.0814
7	2.1502	0.05	6.60106	3.0010
8	7.8581	0.05	6.60106	0.2394
9	0.4402	0.05	6.60106	5.7499
10	4.4075	0.05	6.60106	0.7289
11	5.5830	0.05	6.60106	0.1570
12	10.9588	0.05	6.60106	2.8767
13	2.7431	0.05	6.60106	2.2548
14	6.8725	0.05	6.60106	0.0112
15	0.0322	0.05	6.60106	6.5369
16	4.7905	0.05	6.60106	0.4966
17	14.1998	0.05	6.60106	8.7472
18	10.0138	0.05	6.60106	1.7644
19	10.9438	0.05	6.60106	2.8570
20	2.4410	0.05	6.60106	2.6217

Chi-Square Test

N	DF	Chi-Sq	P-Value
132.021	19	80.2537	0.000

O = Observed frequency

E = expected frequency

P-value = 0.000

Conclusion - Reject Ho, We can conclude that the data is not exponentially distributed (Reason P-value is less than 0.05)

orchestra answered 2 years ago

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